For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points that belong to the AB line:
[tex](x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope [tex]m = 3[/tex], then the equation will be of the form:
[tex]y = 3x + b[/tex]
We substitute the given point and find b:
[tex](x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b[/tex]
Finally, the equation is:
[tex]y = 3x + 2[/tex]
Answer:
[tex]y = 3x + 2[/tex]
